I am dealing with sets of vectors { x 1 , x 2 , x 3 , … , x m } from some abstract vector space V . Occasionally, V = R n an I need to address the elements these vectors e.g. sum over all elements of the vector x j . However, the subindex is already used to denote a specific vector.Is there a common notation address the elements of a vector? E.g. x j [ i ] or x j i or x j ( i ) ?

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I am dealing with sets of vectors             {            x    1    ,      x    2    ,      x    3    ,  …  ,      x    m              }       from some abstract vector space       V  . Occasionally,       V    =            R        n   an I need to address the elements these vectors e.g. sum over all elements of the vector       x    j  . However, the subindex is already used to denote a specific vector.Is there a common notation address the elements of a vector? E.g.       x    j    [  i  ] or       x    j    i   or       x    j          (      i      )      ?

Malierb6 · Accepted Answer

In Banach spaces, where we often consider elements of sequence spaces (e.g.   x  ∈      c    0   so that   x  =  (      x    1    ,      x    2    ,  …  )) the problem of indexing comes up a lot. Typically when we need to index into a sequence of sequences we use       x    j    (  n  ) to indicate the       n                  t        h             component of the       j                  t        h             element of the master sequence. I would disagree with Wuestenfux here and say that this is reasonably standard in Banach Space Theory.Other suggestions, such as raised indices (      x    j    i  ) run into problems when you need to consider powers of the series, and multiple sub-indices (      x          i      ,      j      ) can get confusing and hard to read (there&#039;s a Banach space called Schreier space where some of the proofs require considering indices j such that       p                  n        k            +      1        ≤  j  ≤      p                  n                  k          +          1                    +      1       which is not only hard to read, but hard to think about!). Provided you are clear that       x    j   refers to a sequence and not a function you shouldn&#039;t have much difficulty with people understanding       x    j    (  n  )

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